CISM-ECCOMAS International Summer School on "Novel Finite Element Technologies for Solids and Structures"
September 18, 2017 — September 22, 2017
- Paulo de Mattos Pimenta (Polytechnic School - University of Sao Paulo, São Paulo, Brazil)
- Jörg Schröder (University of Duisburg-Essen, Essen, Germany)
A majority of today’s engineering applications can be solved by finite element technologies. Nevertheless, for several important problems, the application of standard numerical simulation techniques, as for example the Galerkin method, is limited due to drawbacks like numerical stability issues, locking phenomena and non-smoothness of the solution. In order to improve capabilities and the reliability of numerical simulations, advanced finite element methods are a major part of today’s research in the field of mechanics and mathematics.
Due to the progress in this emerging field the objective of this course is to present new ideas in the framework of novel finite element discretization schemes. Thereby the lectures are focused as well on the mechanical as also on the mathematical background. Here, recent developments in mixed finite element formulations in solid mechanics and on novel techniques for flexible structures at finite deformations will be emphasized. A special focus will aim on the implementation and automation aspects of these technologies. The presented automation processes will pay attention to the application of automatic differentiation technique, combined with the symbolic problem description, automatic code generation and code optimization. The combination of these approaches leads to highly efficient numerical codes, which are fundamental for reliable simulations of complicated engineering problems.
The presented modeling techniques cover a huge range of advanced finite element techniques. The special topics of this course are: The isogeometric concept applied to solid and shell structures, novel C1-continuous finite element technologies for Kirchhoff-Love shell models, robust mixed and discontinuous Galerkin methods for solids, plates and shells including strong material anisotropies, flexible body systems considering holonomic and non-holonomic constrains, the Virtual Finite Element Method and concepts of robust preconditioning techniques for large scale problems. Furthermore, the course introduces the theory and application of AceGen: A multi-language and multi-environment tool for highly efficient numerical code generation. These techniques encounter a wide range of applications from elasticity, viscoelasticity, plasticity, and viscoplasticity in classical engineering disciplines, as for instance, civil and mechanical engineering, as well as in modern branches as biomechanics and multiphysics.
The course is intended for doctoral and postdoctoral researchers in civil and mechanical engineering, applied mathematics and physics as well as industrial researchers, which are interested in conducting research in the topics of advanced mixed Galerkin FEM, structural finite element methods, mathematical analysis as well as formulations and applications of these methods to finite strain or coupled problems. Through this course, the students can gain a deep insight into interesting discussions, based on the different backgrounds of the lecturers and it is a must for all that are interested and/or involved in advanced finite element technologies.
The course is closely related to the Priority Program 1748 “Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis” funded by the German Research Foundation.